The Newport company has worked worked on numerous landmark structures, including the roof of the London Olympics Aquatics Centre.
Its collapse puts 400 jobs at risk.
Managing director Andrew Hoppé issued a statement saying: "It is with great regret that we have had to come to the decision to place the business in the hands of the administrators.
"Working with key business partners and the Welsh government, we have exhausted every option to sustain the business for the future. We will be looking to mitigate how this development may impact on the workforce.
"We are proud of all we have achieved over 40 years of trading and I'd like to take this opportunity to thank our customers, suppliers and other business partners. This is a very sad day. We are a family-run company and have a hugely committed, highly capable workforce.
"Above all I would like to thank them for their fantastic part in the Rowecord story and express our deep regret for the impact this will have on them and their families."
Rowecord was founded by chairman Ben Hoppé and at peak had more than 600 staff and a turnover of £75m.